Qi-Wei Ge

Modelling and simulation of signal transductions in an apoptosis pathway by using timed Petri nets

This paper first presents basic Petri net components representing molecular interactions and mechanisms of signalling pathways, and introduces a method to construct a Petri net model of a signalling pathway with these components. Then a simulation method of determining the delay time of transitions, by using timed Petri nets — i.e. the time taken in firing of each transition — is proposed based on some simple principles that the number of tokens flowed into a place is equivalent to the number of tokens flowed out. Finally, the availability of proposed method is confirmed by observing signalling transductions in biological pathways through simulation experiments of the apoptosis signalling pathways as an example.

WF-Net Based Modeling and Soundness Verification of Interworkflows

This paper deals with WF-net based modeling and verification of interorganizational workflows (interworkflows for short) based on the protocol of WfMC. In the protocol, there are three patterns of interoperability: Chained, Nested, and Parallel synchronized; and an interworkflow is constructed by using those interoperability patterns. We first give a WF-net based modeling method. In this modeling method, the three interoperability patterns are respectively expressed in terms of WF-nets. They enable us to model a given interworkflow as a WF-net by connecting WF-nets representing its constituent workflows. We also indicate that if free choice WF-nets are connected by means of any combination of the three patterns then the resultant WF-net is asymmetric choice. Next we discuss verification of WF-nets obtained through the modeling method. Intuitively, a WF-net is said to be sound if, for any case, the initial state is always transformed to the final state. Unfortunately, even if every constituent WF-net is sound FC, the resultant WF-net is not always sound. We give a sufficient condition of non-soundness checkable in polynomial time. We also show that if they are connected by only the Nested pattern then the resultant WF-net is sound.

A Flexible and Efficient Workflow Change Type: Selective Shift

This paper proposes a new change type for dynamic change of workflows, named Selective Shift. Workflow technology is being introduced in many companies. Workflows are business processes that allow for computerized support. The goal of workflow technology is to process workflow instances, called cases, as efficiently as possible. Companies need to change their workflows in order to adapt them to various requirements. Dynamic change is to change workflows having running cases. The most important issue in dynamic change is how running cases should be handled. Ellis et al. and Sadiq et al. have proposed change types that prescribe how to handle running cases. Their change types handle running cases collectively. If a change type can handle running cases separately, the change type would be more flexible and efficient than the conventional change types. However, there is no any change type that can handle running cases separately. Selective Shift to be proposed can handle running cases separately. We first present the concept and definition of Selective Shift. Then we give a method to handle running cases separately. Furthermore we give methods to handle running cases so that dynamic change becomes most efficient on one evaluation measure, called change time. Finally we compare Selective Shift with the conventional change types on change time by using 270 examples of dynamic change.

On determining firing delay time of transitions for Petri net based signaling pathways by introducing stochastic decision rules.

Parameter determination is important in modeling and simulating biological pathways including signaling pathways. Parameters are determined according to biological facts obtained from biological experiments and scientific publications. However, such reliable data describing detailed reactions are not reported in most cases. This prompted us to develop a general methodology of determining the parameters of a model in the case of that no information of the underlying biological facts is provided. In this study, we use the Petri net approach for modeling signaling pathways, and propose a method to determine firing delay times of transitions for Petri net models of signaling pathways by introducing stochastic decision rules. Petri net technology provides a powerful approach to modeling and simulating various concurrent systems, and recently have been widely accepted as a description method for biological pathways. Our method enables to determine the range of firing delay time which realizes smooth token flows in the Petri net model of a signaling pathway. The availability of this method has been confirmed by the results of an application to the interleukin-1 induced signaling pathway.

Complexity and a Heuristic Algorithm of Computing Parallel Degree for Program Nets with SWITCH-Nodes

This paper deals with computation of parallel degree, PARAdeg, for (dataflow) program nets with SWITCH-nodes. Ge et al. have given the definition of PARAdeg and an algorithm of computing PARAdeg for program nets with no SWITCH-nodes. However, for program nets with SWITCH-nodes, any algorithm of computing PARAdeg has not been proposed. We first show that it is intractable to compute PARAdeg for program nets with SWITCH-nodes. To do this, we define a subclass of program nets with SWITCH-nodes, named structured program nets, and then show that the decision problem related to compute PARAdeg for acyclic structured program nets is NP-complete. Next, we give a heuristic algorithm to compute PARAdeg for acyclic structured program nets. Finally, we do experiments to evaluate our heuristic algorithm for 200 acyclic structured program nets. We can say that the heuristic algorithm is reasonable, because its accuracy is more than 96% and the computation time can be greatly reduced.

Dead Problem of Program Nets

In this paper, we discuss a new property, named dead, of (dataflow) program nets. We say that a node of a program net is dead iff the node cannot fire once in any possible firing sequence, and furthermore the program net is partially dead. We tackle a problem of deciding whether a given program net is partially dead, named dead problem. Program nets can be classified into four subclasses: general, acyclic, SWITCH-less, and acyclic SWITCH-less nets. For each subclass, we give a method of solving dead problem and its computation complexity. Our results show that (i) acyclic SWITCH-less nets are not partially dead; (ii) for SWITCH-less nets, dead problem can be solved in polynomial time; (iii) for acyclic nets and general nets, dead problem is intractable.

Performance Evaluation on Worst Change Time of Flush and SCO Dynamic Changes for State Machine WF-Nets*This paper was presented at Session THB1 (Linear//Nonlinear Systems (1)) of ITC-CSCC 2005.

This paper deals with the performance evaluation of two types of dynamic change, called Flush and SCO (Synthetic Cut-Over), for state machine WF-nets. As an evaluation measure of dynamic change for marked graph WF-nets, change time has been used. We first generalize change time so as to apply it to dynamic change for state machine WF-nets. By using its maximum value, we evaluate the worst-case of dynamic change for state machine WF-nets. We call the maximum value as worst change time. Then under the same assumptions as our previous studies, we give methods of calculating worst change time of Flush and SCO dynamic changes. We also clarify the relation on worst change time between them. Finally we evaluate them by comparing the values of worst change time for an actual example of dynamic change.

On generating elementary T-invariants of Petri nets by linear programming

T-invariants represent periodic behaviors of Petri nets and elementary T-invariants represent fundamental periodic behaviors that cannot be divided into smaller ones. To reveal the dynamic behavior of a system modeled by a Petri net, generating elementary T-invariants is indispensable. For a given Petri net, there may be an enormous number of elementary T-invariants and so generally generating all the elementary T-invariants would take too much computation time and storage. In this paper, we discuss how to apply linear programming techniques to compute elementary T-invariants. As a result, we propose a new efficient method of computing all the elementary T-invariants of a given Petri net with less storage.

Dependent Shrink of Transitions for Calculating Firing Frequencies in Signaling Pathway Petri Net Model

Despite the recent rapid progress in high throughput measurements of biological data, it is still difficult to gather all of the reaction speed data in biological pathways. This paper presents a Petri net-based algorithm that can derive estimated values for non-valid reaction speeds in a signaling pathway from biologically-valid data. In fact, these reaction speeds are reflected based on the delay times in the timed Petri net model of the signaling pathway. We introduce the concept of a “dependency relation” over a transition set of a Petri net and derive the properties of the dependency relation through a structural analysis. Based on the theoretical results, the proposed algorithm can efficiently shrink the transitions with two elementary structures into a single transition repeatedly to reduce the Petri net size in order to eventually discover all transition sets with a dependency relation. Finally, to show the usefulness of our algorithm, we apply our algorithm to the IL-3 Petri net model.

An algorithm to estimate delay times in petri net models of signaling pathways with experimental data

In this paper, we propose an algorithm to estimate delay times in a Petri net model of signaling pathways based on biological experimental data. Firstly, we demonstrate a modeling method of signaling pathways with discrete Petri net using ErbB4 signaling pathway. Then, we propose a delay time estimation algorithm for Petri net models with experimental data. The estimated delay times are assigned to the transitions of the Petri net model of the ErbB4 signaling pathway that is simulated on Cell Illustrator 3.0. The simulation results are evaluated by comparing with the experimental data.